Exercise_11:Hyperion

Abstract

Use principally the Newton's gravitation law to study the solar system. We focus on the three problems,first,simulating the two body locomotion problem; second, investigating the inverse-square force law precisely and see the variation change with the ellipticity; third, using the general relativity adjust the force law and then study the mercury precession, see the variation of eccentricity versus precession angular speed.

Background

Saturn is the sixth planet from the Sun and the second-largest in the Solar System, after Jupiter. It is a gas ,giant with an average radius about nine times that of Earth. Although only one-eighth the average density of Earth, with its larger volume Saturn is just over 95 times more massive.Saturn is named after the Roman god of agriculture; its astronomical symbol (♄) represents the god's sickle.

Hyperion , also known as Saturn VII (7), is a moon of Saturn discovered by William Cranch Bond, George Phillips Bond and William Lassell in 1848. It is distinguished by its irregular shape, its chaotic rotation, and its unexplained sponge-like appearance. It was the first non-round moon to be discovered.

Mian body

the two body problem:

it even have more detailed structure:

then we study the trajectory to say whether these instability is true.
then we study the trajectory to say whether these instability is true.

Acknowledgement

Nicholas J.Giordano, Hisao Nakanishi.Computational physics.清华大学出版社